Yes, the Queen took the throne at the twilight of the British Empire. But it was in the midst of the Malayan emergency, the Mau Mau uprising, the Suez crisis was on the horizon, and South Africa had just launched the apartheid regime. Those were all, in different ways, attempts to stamp out democratic independence. Britain didn't relinquish its sub-Saharan African and Caribbean territories until the 1960s. You cannot cleanly separate the Queen from the empire which she crowned.